(5 pts) Which of the direction fields corresponds to the system x -Cx, where C is a 2x2 matrix with eigenvalues-l t 2i with corresponding eigenvector v c. 01 [2i
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4. (15 pts Consider the following direction fields IV VI (5 pts)Which of the direction fields corresponds to the system x -Ax, where A is a 2x2 matrix with eigenvalues λ,--1 and λ2-2 and correspondin...
5. The following matrix B has known eigenvalues λ1-1 and λ2-6. 10a-1 B-0b-23 c30 0 Where...
5. The following matrix B has known eigenvalues λ1-1 and λ2-6. 10a-1 B-0b-23 c30 0 Where a, b and c real numbers and vis the eigenvector associated with the eigenvalue A1. e. Determine as many of a, b, and c as you can. f.Determine the third eigenvalue, if possible. g.Determine the second and third eigenvectors, if possible.
Consider the 2×22×2 matrix AA given by A=1−2[−5−1−1−5].A=1−2[−5−1−1−5].. Find the eigenvalues λ+λ+ and λ−λ−, larger and...
Consider the 2×22×2 matrix AA given by
A=1−2[−5−1−1−5].A=1−2[−5−1−1−5].. Find the eigenvalues λ+λ+ and
λ−λ−, larger and smaller or equal or conjugate, respectively, of
the matrix AA,
I am really stuck on parts b and c so any help would be greatly
appreciated!
(10 points) 5 Consider the 2 x 2 matrix A given by A al -}] 1 a. (2/10) Find the eigenvalues l_ and _, larger and smaller or equal or conjugate, respectively, of the matrix A, + =...
0 -2 - The matrix A -11 2 2 -1 has eigenvalues 5 X = 3,...
0 -2 - The matrix A -11 2 2 -1 has eigenvalues 5 X = 3, A2 = 2, 13 = 1 Find a basis B = {V1, V2, v3} for R3 consisting of eigenvectors of A. Give the corresponding eigenvalue for each eigenvector vi.
please help !!!! 10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a) Show that v = | 1 | and w = 1-2) are eigenvectors of A. b) Identify the defective eigenvalu...
please help !!!!
10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a) Show that v = | 1 | and w = 1-2) are eigenvectors of A. b) Identify the defective eigenvalue of A, and find a corresponding generalized eigenvector Ax c) Write out the general solution of x
10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a)...
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: 4 = 2...
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: 4 = 2 with vi = and |_ G 12 = -2 with v2 = Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: x(t) (50) = C1 + C2 e e B. In fundamental matrix form: (MCO) = I: C. As two equations: (write "c1" and "c2" for C1 and c2) x(t) = yt) =
Suppose a dynamical system is modeled with a difference equation x- Ax-1 k0.1.2.3.... where 4 2 8...
Linear Algebra Question
Suppose a dynamical system is modeled with a difference equation x- Ax-1 k0.1.2.3.... where 4 2 8 .2 1 1 7 Three linearly independent eigenvectors of A are The initial condition is x: In the manner discussed in class, express the initial condition as a linear combination of the eigenvectors of A. Then construct the general solution to the difference equation using the eigenvalues and eigenvectors of A. Finally determine the long term steady-state solution to the...
Question B3 (10 marks) Solve the following homogeneous system of first order ODE dai di da dt x,(0)=2. Makesures ou usethe initial with the initial conditions (0):0 0)=1, is in the following for...
Question B3 (10 marks) Solve the following homogeneous system of first order ODE dai di da dt x,(0)=2. Makesures ou usethe initial with the initial conditions (0):0 0)=1, is in the following form Hint: It is given that one of the solutions of the above system Useful formulas Case 1: A only have distinct roots for λ General solution is ,n) are the coresponding eigenvectors where K, (where i = 1,2, Case 2: For a system of n equations, the...
[18 Point Problem 5: Consider the following (2 x 2) matrix A: 1-4 -1] A= 13...
[18 Point Problem 5: Consider the following (2 x 2) matrix A: 1-4 -1] A= 13 2 a) Find the eigenvalues and the eigenvectors for the matrix. b) Compute the magnitude of the eigenvectors corresponding to both eigenvalues where a = 1. Observing your results, what conclusion can you draw. ('a' is the complex number replacing the free variables 11 or 12)
5. The following matrix B has known eigenvalues λ1-1 and λ2-6. 10a-1 B-0b-23 c30 0 Where a, b and c real numbers and vis the eigenvector associated with the eigenvalue A1. e. Determine as many of a, b, and c as you can. f.Determine the third eigenvalue, if possible. g.Determine the second and third eigenvectors, if possible.
Consider the 2×22×2 matrix AA given by
A=1−2[−5−1−1−5].A=1−2[−5−1−1−5].. Find the eigenvalues λ+λ+ and
λ−λ−, larger and smaller or equal or conjugate, respectively, of
the matrix AA,
I am really stuck on parts b and c so any help would be greatly
appreciated!
(10 points) 5 Consider the 2 x 2 matrix A given by A al -}] 1 a. (2/10) Find the eigenvalues l_ and _, larger and smaller or equal or conjugate, respectively, of the matrix A, + =...
0 -2 - The matrix A -11 2 2 -1 has eigenvalues 5 X = 3, A2 = 2, 13 = 1 Find a basis B = {V1, V2, v3} for R3 consisting of eigenvectors of A. Give the corresponding eigenvalue for each eigenvector vi.
please help !!!!
10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a) Show that v = | 1 | and w = 1-2) are eigenvectors of A. b) Identify the defective eigenvalue of A, and find a corresponding generalized eigenvector Ax c) Write out the general solution of x
10. 20 points Consider the homogeneous system x' Ax, where 4 0 0 A 1 0 2 02 3 a)...
(1 point) Suppose that the matrix A has the following eigenvalues and eigenvectors: 4 = 2 with vi = and |_ G 12 = -2 with v2 = Write the solution to the linear system r' = Ar in the following forms. A. In eigenvalue/eigenvector form: x(t) (50) = C1 + C2 e e B. In fundamental matrix form: (MCO) = I: C. As two equations: (write "c1" and "c2" for C1 and c2) x(t) = yt) =
Linear Algebra Question
Suppose a dynamical system is modeled with a difference equation x- Ax-1 k0.1.2.3.... where 4 2 8 .2 1 1 7 Three linearly independent eigenvectors of A are The initial condition is x: In the manner discussed in class, express the initial condition as a linear combination of the eigenvectors of A. Then construct the general solution to the difference equation using the eigenvalues and eigenvectors of A. Finally determine the long term steady-state solution to the...
Question B3 (10 marks) Solve the following homogeneous system of first order ODE dai di da dt x,(0)=2. Makesures ou usethe initial with the initial conditions (0):0 0)=1, is in the following form Hint: It is given that one of the solutions of the above system Useful formulas Case 1: A only have distinct roots for λ General solution is ,n) are the coresponding eigenvectors where K, (where i = 1,2, Case 2: For a system of n equations, the...
[18 Point Problem 5: Consider the following (2 x 2) matrix A: 1-4 -1] A= 13 2 a) Find the eigenvalues and the eigenvectors for the matrix. b) Compute the magnitude of the eigenvectors corresponding to both eigenvalues where a = 1. Observing your results, what conclusion can you draw. ('a' is the complex number replacing the free variables 11 or 12)
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